Rig Edit Squashing Hands?
I would try and place the armature correctly within the mesh before pairing. Then when pairing select 'automatic weights' to initialize the 'painted weights' for each bone. Then it is useful to go into 'Weight Painting Mode' select the problematic bone areas and try to paint the weights so that each bone only effects its nearby mesh.

This is a great series about rigging. The episode I've linked to is about Weight Painting. Highly recommended.
https://www.youtube.com/watch?v=G3gIN4dJYw4

*It looks like your middle finger bone is deforming the mesh of the other fingers.

Good Luck!